时滞执行器饱和Markov跳变系统的有限时间镇定

讨论了含执行器饱和的离散时滞Markov跳变系统在未知但有界扰动的情况下,针对系统模态转移概率部分未知的系统进行有限时间镇定的分析和研究。利用构造的Lyapunov函数和饱和非线性处理技术,对具有执行器饱和的离散时滞Markov系统进行研究,并提出了系统状态有限时间镇定的充分条件,结合线性矩阵不等式的方法,设计并实现了有限时间镇定状态反馈控制器。通过数值仿真,示例验证了该设计方法的有效性及潜在的应用性。     

一类模糊双线性跳变系统的随机镇定问题

研究了一类模糊双线性跳变系统的随机镇定问题. 采用T-S模糊建模技术来构建模糊双线性跳变模型, 然后通过并行分布补偿 (Parallel distributed compensation, PDC) 方法和选择合适的模糊隶属度函数, 将整个非线性控制器表示为一组局部线性控制器的模糊综合. 此外, 还推导出了保证闭环模糊双线性跳变系统随机稳定的充分条件, 并且这些条件最终可归结为一组线性矩阵不等式 (Linear matrix inequalities, LMIs)的可行性问题. 最后, 连续搅拌反应釜(Continuous stirred tank reactor, CSTR)系统的数值示例表明该设计方法的合理性和有效性.     

对带控制器饱和的Markovian跳跃双线性系统稳定时滞估计

研究了带有饱和控制器的时滞Markovian跳跃双线性系统随机镇定问题. 文章先给出了采用无记忆控制的相应无时滞系统局部指数稳定的充分性条件, 然后给出了采用该无记忆控制的时滞系统保持随机稳定性的最大时滞上界估计. 数值算例验证了该方法的有效性.     

执行器饱和的线性连续系统的镇定

针对控制系统中广泛存在饱和问题,主要研究执行器饱和线性连续系统的镇定问题并进行吸引域估计。首先根据Finsler’s引理和Lyapunov函数方法研究系统稳定的充分条件,得到执行器饱和控制系统稳定的新判据。其次,在稳定条件下,应用凸组合方法和新引入的自由权矩阵使得系统吸引域估计具有更小的保守性,将所得非线性矩阵不等式转化为线性矩阵不等式,给出求解最大吸引域的优化方法和状态反馈控制器的设计方案。最后通过仿真算例验证结果的有效性和可行性。     

带有执行器饱和的变时滞Markovian 跳变系统的DOBC控制

针对一类转移概率部分未知的Markovian跳变系统,考虑系统中存在时变时滞以及执行器饱和的情况,研究此类系统基于干扰观测器的抗干扰控制(Disturbance-observer-based-control,DOBC)问题.首先,分析带有扰动估计误差的闭环系统的随机稳定性,通过构建适当的模态依赖型Lyapunov-Krasovskii(L-K)泛函并引入自由权矩阵,给出闭环系统的随机稳定性判据;然后,将控制器增益以及观测器增益的求解问题转化为带有线性矩阵不等式约束的可行性问题,并通过迭代优化算法得到最大吸引域的估计值;最后,通过仿真算例,验证所提出方法的正确性和有效性.     

跳变双线性随机离散组合系统的保成本分散控制

研究一类跳变双线性随机离散组合系统的保成本分散控制问题．首先给出问题可解的充分条件,然后基于线性矩阵不等式方法设计保成本分散状态反馈控制律．理想的保成本分散状态反馈控制器可通过应用现有的软件,求解一组线性矩阵不等式而得到．仿真例子说明了该方法的有效性.     

奇异线性系统在执行器饱和受限下不变集条件的改进

本文考虑饱和线性反馈下奇异线性系统扩大吸引域估计的问题.根据每个输入是否饱和,将输入空间分成若干子区域.在每个子区域内部,系统模型中没有显示的部分状态的时间导数可被显式表达.利用含有全部系统状态的二次Lyapunov函数,建立一组双线性矩阵不等式形式的改进的不变集条件.该组条件下,二次Lyapunov函数的水平集可诱导出一个吸引域估计.为得到最大的吸引域估计,构建了以这些双线性矩阵不等式为约束条件的优化问题,并为其求解给出了迭代算法.仿真结果表明本文得到的吸引域估计明显大于现有结果.     

一类时不变双线性系统的可镇定条件

讨论了一类时不变双线性系统的状态反馈镇定问题,利用系统矩阵线性无关的特征向量,给出了双线性系统的状态反馈控制器设计方法,并且,通过分析一个特定的二次方程组的唯一性,讨论了双线性系统的可镇定条件。     

具有饱和执行器的时滞广义系统的鲁棒控制

利用李亚普诺夫方法研究了时滞广义系统、不确定广义系统和不确定时滞广义系统的鲁棒镇定问题.首先设计了时滞广义系统的具有饱和执行器的控制律,并给出其闭环系统渐近稳定的充分条件.对不确定项是范数有界的不确定广义系统,给出其控制器的设计方法和闭环系统渐近稳定的充分条件.在此基础上,进一步给出了不确定时滞广义线性系统的镇定条件.最后,给出了一个数值算例来说明方法的有效性.     

Gain scheduling consensus of multi-agent systems subject to actuator saturation

ABSTRACT

This paper presents a gain scheduling approach for achieving the consensus tracking of multi-agent systems with actuator saturation. We first construct a series of nesting ellipsoid invariant sets associated with consensus errors. When the consensus errors stay between the two ellipsoid invariant sets, the feedback gains keep constant, but when the consensus errors enter into the smaller ellipsoid invariant set, the feedback gains abruptly become larger. By combining this gain scheduling technique and the parametric Lyapunov equations, we, respectively, design state and output feedback gain scheduling protocols. Their main advantage, in comparison with the fixed case, is that the convergence rate of consensus tracking can be enhanced by scheduling the gain parameters. Numerical simulations verify the effectiveness of theoretical analysis.     

Stability and stabilization of discrete-time periodic linear systems with actuator saturation

This paper is concerned with the problems of stability and stabilization for discrete-time periodic linear systems subject to input saturation. Both local results and global results are obtained. For local stability and stabilization, the so-called periodic invariant set is used to estimate the domain of attraction. The conditions for periodic invariance of an ellipsoid can be expressed as linear matrix inequalities (LMIs) which can be used for both enlarging the domain of attraction with a given controller and synthesizing controllers. The periodic enhancement technique is introduced to reduce the conservatism in the methods. As a by-product, less conservative results for controller analysis and design for discrete-time time-invariant systems with input saturation are obtained. For global stability, by utilizing the special properties of the saturation function, a saturation dependent periodic Lyapunov function is constructed to derive sufficient conditions for guaranteeing the global stability of the system. The corresponding conditions are expressed in the form of LMIs and can be efficiently solved. Several numerical and practical examples are given to illustrate the theoretical results proposed in the paper.     

Stability analysis for linear discrete-time systems subject to actuator saturation

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.     

Control of periodic sampling systems subject to actuator saturation

In this paper, the control problem of linear systems with periodic sampling period subject to actuator saturation is considered via delta operator approach. Using periodic Lyapunov function, sufficient conditions of local stabilization for periodic sampling systems are given. By solving an optimization problem, we derive the periodic feedback control laws and the estimate of the domain of attraction. As the saturation function sat(·) belongs to the sector [0,1], sufficient conditions are derived by constructing saturation‐dependent Lyapunov functions to ensure that the periodic sampling system is globally asymptotically stable. A numerical example is given to illustrate the theoretical results proposed in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis and design for singular discrete linear systems subject to actuator saturation

A method to estimate the domain of attraction for a singular discrete linear system under a saturated linear feedback is established. Simple conditions are derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant. These conditions are expressed in terms of linear matrix inequalities. The largest contractively invariant ellipsoid can also be determined by solving an optimization problem with linear matrix inequality constraints. This result is extended to the design of feedback gain that results in the largest contractively invariant ellipsoid, which is also a linear matrix inequality optimization problem. A numerical example demonstrates the applicability and effectiveness of the presented method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

The design of robust H-infinity controller for uncertain discrete-time Markovian jump systems with actuator saturation is addressed in this paper. The parameter uncertainties are assumed to be norm-bounded. Linear matrix inequality (LMI) conditions are proposed to design a set of controllers in order to satisfy the closed-loop local stability and closed-loop H-infinity performance. Using an LMI approach, a set of state feedback gains is constructed such that the set of admissible initial conditions is enlarged and formulated through solving an optimization problem. A numerical example is given to illustrate the effectiveness of the proposed methods.     

Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances

This paper considers the design of output tracking systems subject to actuator saturation and integrator windup. An optimization-based approach is developed to design feedback and anti-windup gains of a controller structure involving intelligent integrators. The design goal is to increase stability region and output tracking and disturbance rejection ability of the closed-loop system.     

Semi-global stabilization with guaranteed regional performance of linear systems subject to actuator saturation

For a linear system under a given saturated linear feedback, we propose feedback laws that achieve semi-global stabilization on the null controllable region while preserving the performance of the original feedback law in a fixed region. Here by semi-global stabilization on the null controllable region we mean the design of feedback laws that result in a domain of attraction that includes any a priori given compact subset of the null controllable region. Our design guarantees that the region on which the original performance is preserved would not shrink as the domain of attraction is enlarged by appropriately adjusting the feedback laws. Both continuous-time and discrete-time systems will be considered.     

An analysis and design method for linear systems subject to actuator saturation and disturbance

We present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback. A simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant. This condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis. Moreover, the condition can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can easily be used for controller synthesis. This condition is then extended to determine the invariant sets for systems with persistent disturbances. LMI based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements. The effectiveness of the developed methods is illustrated with examples.